You compared pushing a woman to pushing a "kid" (your original phrase). There are two reasons a kicking grown man shouldn't shove a kid standing on a race course:
1) The kid might tumble over and smash his head on the ground.
2) The kid could be excused for not understanding that he was in a bad spot.
Neither of these is applicable to an athletic woman.
So, if a guy "plowed over a kid" on a race course, I bet that few would defend him (and rightly so). However, this thread is not about a kid, so I don't understand what you're getting at.
No, you did not apologize (unless you really did kill him?). You used the word sorry in an expression of sympathy. Like many english words, sorry can be used multiple ways.
Obviously this guy should have tried to avoid the woman. Your right, too, he probably should have also given her some kind of apology, mostly to defuse the situation lest she have some crazy friend who wants to smear the guy across the internet.